Ca = estimated hourly cost of automation ($/hr)
rfoh = factory overhead rate.
The hourly estimated cost of the automation can be determined from the equation
Ca = (CIfcr)/ha,
where
| C I | = | initial cost of the automation ($) |
| f cr | = | capital recovery factor |
| ha | = | time that machine is in operation annually (hr). |
The initial cost of the automation (CI) will be known and hours of machine operation annually (ha) can be readily determined. The capital recovery factor (fcr) is determined by the equation
fcr = r(1 + r)n / [(1 + r)n − 1],
where
r = desired rate of return (%)
n = number of years of the service life of the machine.
Figure 2-4 Typical factory overhead costs
Factory overhead rate (rfoh) is the ratio of factory overhead costs to those of the machine under consideration. This is found by distributing the overhead over some variable such as direct labor costs. Typical factory overhead costs are given in Figure 2-4. For any given factory this can be accomplished by taking all of the overhead costs of the firm for one year and dividing it by the total cost spent on direct labor. The formula for this calculation is:
rfoh = Cfoh/Cdl,
where
| C foh | = | annual cost of factory overhead ($/yr) |
| C dl | = | annual direct labor costs ($/yr). |
The following example demonstrates the use of these formulas.
Example 2.12
An automated work cell is being considered to replace an existing process. The cell will cost $150,000 to purchase and is anticipated to have a 4-year service life. The machine will operate for 2080 hours per year. The company spent $2,300,000 on factory overhead and $6,500,000 on direct labor costs last year. Estimate the hourly capital cost to operate the new automated work cell if the manufacturing firm desires a 15% return on its investment.
Solution
The governing equations are
| C c | = | Ca(1 + rfoh ) |
| C a | = | (CIfcr)/ha |
| f cr | = | r(1 + r)n /[(1 + r)n − 1] |
| r foh | = | Cfoh/Cdl. |
The values are given as
| r foh | = | 35% |
| C I | = | $150,000 |
| h a | = | 2080 hr |
| r | = | 15% |
| n | = | 4 yr |
| C foh | = | $2,300,000/yr |
| C dl | = | $6,500,000/yr. |
First, calculate capital recovery factor:
| f cr | = | r(1 + r)n/[(1 + r)n − 1] |
| = | 0.15(1 + 0.15)4/[(1 + 0.15)4 − 1) | |
| = | (0.15)(1.749)/(1.749 − 1) = 0.26235/0.749 = 0.3503. |
Next, calculate the estimated hourly rate of the work cell (Ca):
Ca = CIfcr/ha = ($150,000)(0.3503)/2080 hr = $25.26/hr.
Calculate factory overhead rate:
rfoh = ($2,300,000/yr)/($6,500,000/yr) = 35.4%.
Finally, calculate the hourly capital cost:
Cc = Ca(1 + rfoh ) = ($25.26/hr)(1 + 0.354) = $34.20/hr.
Thus, the estimated capital cost for operating the new automated work cell is $34.20/hr.
2.5 Comparing Alternatives with Productivity Calculations
Section 2.2 demonstrated the basic procedure for calculating the productivity of a process. Sections 2.3 and 2.4 demonstrated how to quantify the output and inputs of a process for use in the productivity calculations. This section is devoted to developing a methodology of performing the actual comparison of the alternatives. This essentially involves organizing the data in a logical, comprehensive manner in which the alternatives can be directly compared. The author has found that this is easily accomplished by organizing the data in a spreadsheet as shown in Figure 2-5.
Figure 2-5 Combined productivity